Theory of structured multiphase mixtures
This work deals with multiphase mixtures characterized by interfaces between phases as opposed to single phase, multicomponent mixtures. Continuum field equations are used for each phase volume, the boundary conditions between the phases being provided by another set of field equations. Averaging of local macroscopic equations is taken over suitable time and space segments and the averaged variables appear in the mixture dynamics and energetics. Structural characteristics are accounted for by additional transport equations leading to additional balance equations. There is overlap with single phase, multi-component mixture theories only in special situations. The book is self-contained in that it contains an appendix in which relevant results on linear vector spaces, vector calculus and tensor representation theorems are quoted. It is comprised of eight chapters: Chapter 1: Historical developments of the subject are outlined. Chapters 2 and 3: The basic mechanical and thermodynamic field equations are developed in chapter 2 and enhanced in chapter 3 by additional transport equations to account for `structure'. Chapter 4: Restrictions imposed on the kinematic, dynamic and thermodynamic variables by the principle of material frame indifference are discussed. Chapter 5: A simplification of the theory is introduced by restricting the motion of a material phase volume to a rotation about its centre of mass and an affine deformation, relative to the same point, which is a pure dilatation. The results are compared with other existing theories of structured multiphase mixtures. Chapter 6: The principles of constitutive theory are developed for different types of mixtures, such as solid and fluid phases. Chapters 7 and 8: Particular constitutive equations are studied and results for two phase mixtures obtained.
principle of material frame indifference
scientific article; zbMATH DE number 108209